I bought a Bluetooth audio receiver module (https://www.ebay.com/itm/373728146920)  for the purpose. The module is powered by USB and has a three prong audio out connector. An alternative output is provided by solder pads. 

The internet radio box already had an internal USB connector for the WiFi modem. The WiFi is not needed any more so I pulled the modem out. Alternatively I could have powered the BT module from +5 and ground pins marked as so on the radio PCBs.

The plan was to connect the audio output from the module to the radio Aux input. The easy way would be to use a male/male cable. Since I didn't have such a cable I cut one from an old head set, providing me with a plug and an open end cable. The head set cable had two wires for each ear. I soldered the ends of the wires to the audio output pads of the module. One to Left, one to Right and the two neutral colored to Ground. The wires are thin and I reinforced them with a blob of hot glue. Soldering removes the insulation of these thin wires.

Then I wrapped the module in a plastic bag, connected a USB cable and pushed the audio jack into the Aux input. And I had a Bluetooth loudspeaker.